Homogenization of many-particle systems

In this project we study the dynamics of a large number of (generalized) particles which interact in order to reduce the surface energy attached to the boundaries of the particles. We consider two model examples. The first is Ostwald Ripening, a fundamental process in the aging of materials, where particles interact through weak long range diffusional interactions. Second, we consider grain growth, where cellular structures in a plycrystalline material coarsen under capillary effects. here the interactions between grains are not weak, but localized. The general aim in this project is to understand the collective behaviour of a large number of particles; of particular interest is whether universal statistical self-similarity arises, whether correlations are built up during the evolution and how they influence the macroscopic picture.